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AIMS Mathematics

2026, Volume 11, Issue 8: 23606-23628. doi: 10.3934/math.2026951
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Research article

Characterizations of pseudo-Schouten symmetric spacetimes with applications to $ f(\mathcal{R}) $ gravity

  • 1.
    Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA
  • 2.
    Department of Mathematics and Statistics, College of Science, University of Jeddah, Jeddah 23890, Saudi Arabia
  • 3.
    Department of Pure Mathematics, University of Calcutta, Ballygaunge Circular Road 35, Kolkata 700019, West Bengal, India
  • 4.
    Department of Mathematics, College of Science, King Saud University, P. O. Box 2455, Riyadh 11451, Saudi Arabia
  • 5.
    Department of Mathematics, Faculty of Science, Zagazig University, P. O. Box 44519, Zagazig, Egypt
  • 6.
    Faculty of Computers and Information Systems, Egyptian Chinese University, Cairo 4541312, Egypt
  • Published: 03 August 2026

  • MSC : 53B20, 53C25, 53C50, 53C80

  • This paper primarily investigated the geometric and physical properties of pseudo-Schouten symmetric (PSS)q spacetimes. First, we demonstrated that the associated covector $ \omega ^{i} $ of such spacetimes is irrotational, non-accelerating, and satisfies $ \omega ^{i}\mathcal{R}_{ij} = \frac{\mathcal{R}}{2}\omega _{j} $. Next, we examined (PSS)q generalized Robertson-Walker spacetimes. Among various results, we proved that a (PSS)$ _{q} $ generalized Robertson-Walker spacetime is a perfect fluid spacetime. Furthermore, we showed that a (PSS)q spacetime with a Codazzi-type Ricci tensor constitutes a perfect fluid, whereas one with a cyclic parallel Ricci tensor represents a vacuum spacetime. We then established that a (PSS)$ _{q} $ spacetime characterized by a divergence-free Weyl tensor is static. Finally, we explored the physical implications of (PSS)q spacetimes within the framework of $ f\left(R\right) $ gravity, explicitly deriving the corresponding isotropic pressure and energy density.

    Citation: Bang-Yen Chen, Awatif Al-Jedani, Uday Chand De, Nasser Bin Turki, Abdallah Abdelhameed Syied. Characterizations of pseudo-Schouten symmetric spacetimes with applications to $ f(\mathcal{R}) $ gravity[J]. AIMS Mathematics, 2026, 11(8): 23606-23628. doi: 10.3934/math.2026951

    Related Papers:

  • This paper primarily investigated the geometric and physical properties of pseudo-Schouten symmetric (PSS)q spacetimes. First, we demonstrated that the associated covector $ \omega ^{i} $ of such spacetimes is irrotational, non-accelerating, and satisfies $ \omega ^{i}\mathcal{R}_{ij} = \frac{\mathcal{R}}{2}\omega _{j} $. Next, we examined (PSS)q generalized Robertson-Walker spacetimes. Among various results, we proved that a (PSS)$ _{q} $ generalized Robertson-Walker spacetime is a perfect fluid spacetime. Furthermore, we showed that a (PSS)q spacetime with a Codazzi-type Ricci tensor constitutes a perfect fluid, whereas one with a cyclic parallel Ricci tensor represents a vacuum spacetime. We then established that a (PSS)$ _{q} $ spacetime characterized by a divergence-free Weyl tensor is static. Finally, we explored the physical implications of (PSS)q spacetimes within the framework of $ f\left(R\right) $ gravity, explicitly deriving the corresponding isotropic pressure and energy density.



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  • © 2026 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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